Modeling the dynamic and quasi-static compression-shear failure of brittle materials by explicit phase field method

The phase field method is a very effective method to simulate arbitrary crack propagation, branching, convergence and complex crack networks. However, most of the current phase-field models mainly focus on tensile fracture problems, which is not suitable for rock-like materials subjected to compression and shear loads. In this paper, we derive the driving force of phase field evolution based on Mohr-Coulomb criterion for rock and other materials with shear frictional characteristics and develop a three-dimensional explicit parallel phase field model. In spatial integration, the standard finite element method is used to discretize the displacement field and the phase field. For the time update, the explicit central difference scheme and the forward difference scheme are used to discretize the displacement field and the phase field respectively. These time integration methods are implemented in parallel, which can tackle the problem of the low computational efficiency of the phase field method to a certain extent. Then, three typical benchmark examples of dynamic crack propagation and branching are given to verify the correctness and efficiency of the explicit phase field model. At last, the failure processes of rock-like materials under quasi-static compression load are studied. The simulation results can well capture the compression-shear failure mode of rock-like materials.